docs: def Prandtl_von_Karman_Nikuradse(Re):
      r'''Calculates Darcy friction factor for smooth pipes as a function of
      Reynolds number from the Prandtl-von Karman Nikuradse equation as given 
      in [1]_ and [2]_:
      
      .. math::
          \frac{1}{\sqrt{f}} = -2\log_{10}\left(\frac{2.51}{Re\sqrt{f}}\right)
  
      Parameters
      ----------
      Re : float
          Reynolds number, [-]
  
      Returns
      -------
      fd : float
          Darcy friction factor [-]
  
      Notes
      -----
      This equation is often stated as follows; the correct constant is not 0.8,
      but 2log10(2.51) or approximately 0.7993474:
      
      .. math::
          \frac{1}{\sqrt{f}}\approx 2\log_{10}(\text{Re}\sqrt{f})-0.8
  
      This function is calculable for all Reynolds numbers between 1E151 and 
      1E-151. It is solved with the LambertW function from SciPy. The solution is:
      
      .. math::
          f_d = \frac{\frac{1}{4}\log_{10}^2}{\left(\text{lambertW}\left(\frac{
          \log(10)Re}{2(2.51)}\right)\right)^2}
  
      Examples
      --------
      >>> Prandtl_von_Karman_Nikuradse(1E7)
      0.008102669430874914
  
      References
      ----------
      .. [1] Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical
         and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.
      .. [2] McGovern, Jim. "Technical Note: Friction Factor Diagrams for Pipe 
         Flow." Paper, October 3, 2011. http://arrow.dit.ie/engschmecart/28.
      '''
      # Good 1E150 to 1E-150
      c1 = 1.151292546497022842008995727342182103801 # log(10)/2
      c2 = 1.325474527619599502640416597148504422899 # log(10)**2/4
      return c2/float(lambertw((c1*Re)/2.51).real)**2